Question

1. A driver recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up. The following data are the differences between the computer’s and the driver’s calculations for that random sample of 20 records.

For example, the third value is -0.6. That might be a trip where the computer said the gas mileage was 48.1 and the driver computed it as 48.7, giving a difference of -0.6.

The driver wants to determine whether the difference between these two measures is 0 or not. Assume that the standard deviation of a difference is σ = 3.0.

5.0	6.5	−0.6	1.7	3.7	4.5	8.0	2.2	4.9	3.0
4.4	0.1	3.0	1.1	1.1	5.0	2.1	3.7	−0.6	−4.2

(a) (1 pt) State the appropriate H₀and H_a to test this suspicion.

(b) Carry out the test; you must show your work for any credit. Give the P-value, and then state whether you can reject the idea that the calculations are different.

Hint: right after promising that I would never give you a problem with a z statistic outside the range of the table, I have of course given you a problem with a z statistic outside the range of the table. You can use the Excel function normsdist to compute the probability of being to the left of any z statistic, instead of using the table. So you could go into a cell and type = normsdist(1.96) and get back the value 0.975002.

Excel will try to warn you that normsdist is an obsolete function and that you should use norm.s.dist instead. That works, but then you have to type = norm.s.dist(1.96,1) , which seems more annoying than using normsdist.

Answer 1

here the population standard deviation of a difference is given hence we will use standard Z test to test our hypothesis.

a)

alternate hypothesis:

this is a two-tailed test.

b) the sample information about the mean:

Sample mean:

Test statistic:

P value for the two-tailed test

Since the P value is nearly zero it is less than the significance level we generally use for hypothesis testing, i.e .

Hence we can reject the null hypothesis.

Thus we have evidence that the difference is not zero. Thus we can reject the idea that the calculations are not different